Turning incidental triangles to quads
Final:



Overview:

This is the cleanest quad topology I can think of.

I don't know if this is the proper way, but for me it works always the best. Try not to think about quad topology but about Edge Loops and how can you use them along the mesh. If you will work that way, quads will come naturally after some time.

Here you have example with Edge Loop that will allow to control sharpness of the Edge itself combined with Subsurf Modifier.